Curvature pinching for totally real submanifolds of a complex projective space

Abstract

Montiel, Ros and Urbano [{M3}] showed a complete characterization of compact totally real minimal submanifold M of CPⁿ(c) with Ricci curvature S of M satisfying S≥q 3(n-2)c/16. The purpose of this paper is to answer Ogiue's conjecture which the above result remains true under the weaker condition of the scalar curvature ρ of M satisfying ρ≥q 3n(n-2)c/16.